Question

x-3y-4=0 (0,0) find the length of the perpendicular drawn from the point given against the following straight lines​

Answer 1

$\textbf{Given:}$

$\textsf{Point is (0,0)}$

$\mathsf{Line is x-3y-4=0}$

$\textbf{To find:}$

$\textsf{Length of the perpendicular from (0,0) to the line x-3y-4=0}$

$\textbf{Solution:}$

$\textbf{Formula used:}$

$\mathsf{Length\;of\;the\;perpendicular\;from\;(x_1,y_1)\;to\;the\;line}$

$\mathsf{ax+by+c=0\;is\;\left|\dfrac{ax_1+by_1+c}{\sqrt{a^2+b^2}}\right|}$

$\textsf{Length of the perpendicular from (0,0) to the line x-3y-4=0}$

$\mathsf{=\left|\dfrac{ax_1+by_1+c}{\sqrt{a^2+b^2}}\right|}$

$\mathsf{=\left|\dfrac{1(0)-3(0)-4}{\sqrt{1^2+(-3)^2}}\right|}$

$\mathsf{=\left|\dfrac{-4}{\sqrt{1+9}}\right|}$

$\mathsf{=\dfrac{4}{\sqrt{10}}}$

$\mathsf{=\dfrac{2\sqrt{2}{\times}\sqrt{2}}{\sqrt{5}\sqrt{2}}}$

$\mathsf{=\dfrac{2\sqrt{2}}{\sqrt{5}}}$

$\textbf{Answer:}$

$\mathsf{Length\;of\;the\;perpendicular\;is\;\dfrac{2\sqrt{2}}{\sqrt{5}}}$

Answer 2

Answer:

hope the above answer will help you